The seminar meets regularly on Wednesdays at 4pm in Eckhart 202. We also have special seminars during other days. This quarter the seminar will be running remotely via zoom. Access to the zoom links will be provided via the email list. To subscribe or unsubscribe from the email list, you may either go to Camp/PDE email list or contact Cornelia Mihaila.
Mean-field game theory borrows ideas from statistical physics to provide a tractable approximation of very large multi-agent systems. Applications are ubiquitous in today's highly interconnected world, from crowd motion to macroeconomics and distributed robotics. Real-world problems often lead to models which are in high dimension or not fully specified, hence a recent surge of interest for the question of computing solutions with mesh-free and model-free methods. In this talk, we will mainly focus on the question of learning in mean-field games, in cooperative or non-cooperative settings.
Since their introduction around 2006, mean field games (MFGs) have been extensively studied and attracted the interest of many researchers from different backgrounds due to both their interesting mathematical properties and their applicability in a diversity of contexts. This talk will focus on some recent MFG models motivated by crowd motion, called minimal-time MFGs, in which agents want to minimize the time required to reach a given target set. In order to model congestion, the maximal speed of an agent is assumed to depend on the distribution of other agents around their position. After briefly presenting MFGs in general and minimal-time MFGs, the talk will review some recent results in two situations, corresponding to first-order MFGs, in which agents follow deterministic trajectories, and second-order MFGs, in which agents' trajectories are perturbed by additive Brownian motions, assumed to be mutually independent. We will present results on the existence of equilibria, their characterization, their asymptotic behavior, and their regularity properties. We will also discuss recent results which suggest how to tackle the case of minimal-time MFGs with state constraints. This talk is based on joint works with Romain Ducasse, Samer Dweik, Saeed Sadeghi Arjmand, and Filippo Santambrogio.